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#1 2012-10-16 01:17:54

Deon588
Member
Registered: 2011-05-02
Posts: 68

Product of elementary matrices

Hi all.  I think i'm making a mistake somewhere as the matrix I get after multiplying doesn't seem to be invertible and the next question is to find A^-1.  Is this the right way to do this?
Thanks in advance

View Image: elementary matrices.gif

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#2 2012-10-16 01:32:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,387

Re: Product of elementary matrices

Hi;

I am getting:

which can be inverted.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2012-10-16 04:17:36

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Product of elementary matrices

Hi Bobbym any idea where I made a mistake?
Thanks a lot

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#4 2012-10-16 04:28:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,387

Re: Product of elementary matrices

Hi;

Your mistake is in line 3. Check how you multiplied those matrices.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2012-10-16 04:29:47

zetafunc.
Guest

Re: Product of elementary matrices

You multiplied the matrices incorrectly

#6 2012-10-16 04:30:11

zetafunc.
Guest

Re: Product of elementary matrices

Never mind, bobbym was faster.

#7 2012-10-16 05:04:49

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,382

Re: Product of elementary matrices

hi Deon588

Your inverses are correct, so then you need to do the multiplying.

(AB)C = A(BC) for matrices so you have a choice of which pair you multiply first.  But you must preserve order.

eg if AB = D you then do DC not CD.

I'm going to do these both ways in case I choose the way you didn't (if you see what mean)

or


Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#8 2012-10-16 05:12:02

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,382

Re: Product of elementary matrices

and you should find that inverse A = E3.E2.E1

This would be a good check that you have inv A right and that your multiplying is OK.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2012-10-16 23:04:47

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Product of elementary matrices

Hi Bob thanks a lot for all the effort.  I had no idea how to multiply more than 2 matrices so I tried doing all 3 at once...

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#10 2012-10-16 23:10:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,387

Re: Product of elementary matrices

Hi Deon588;

Always break a big problem down into smaller pieces that you know how to do. This top down design is very common in programming. You knew how to do 2 matrices.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11 2012-10-17 00:39:52

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,382

Re: Product of elementary matrices

hi Deon588

I know the rule for multiplying two matrices.  I dareay you could devise a rule for three but it would be hard to remember.  So two at a time is simplest.

You shouldn't assume that matrices can be swopped around like numbers but associativity { (AB)C = A(BC) } does work.

Beware: commutativity doesn't.  { AB ≠ BA }

Did you try my practice suggestion?

and you should find that inverse A = E3.E2.E1

This would be a good check that you have inv A right and that your multiplying is OK.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2012-10-17 08:29:03

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Product of elementary matrices

Yes that was also the next question in the exam paper I did, worked out perfectly at the end smile

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#13 2012-10-17 09:50:27

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,382

Re: Product of elementary matrices

up

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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